The main concern here isn't the dust storm itself. It's the need to keep the rover's heaters operational while maintaining a minimal power level in the batteries. This isn't the first storm that Opportunity has weathered, but it is the worst. According to NASA, the weather event the rover faced in 2007 had an opacity level around 5.5. The estimate for this current storm is somewhere around 10.8.
Opportunity is a hardy little rover, though, and it has continually defied our expectations over the last 15 years. The rover was only designed to last for a 90-day mission, and yet it's still going. Here's hoping that Oppy will continue its trek across the Martian surface for many, many days to come.
Update (June 14th): NASA held a press conference yesterday about Opportunity, and while things are still tentative, there's some good news: the team does believe that Opportunity can survive this storm. The temperature is not expected to drop below the rover's minimum allowable temperature, which means that Oppy has a fighting chance.
Update (June 13th): NASA released more information about Opportunity last night, and things don't look good. The rover's team tried to contact Opportunity yesterday and didn't receive a response. They are assuming this means that the rover's batteries are now critically low, and it's currently in low power fault mode. This means that all subsystems except the mission clock have been shut down, and the computer will automatically reawaken to check power levels.
Due to the size of this dust storm (which now covers about one-quarter of the planet), it's unlikely that Oppy will have the chance to recharge anytime soon. That means that the rover will be in this sleep/wake cycle for a while yet -- until it's able to recharge its batteries enough to send a message home, or until it goes to sleep for good. Hang on, little guy. We're rooting for you.